$\dfrac{ 7b + 6c }{ -4 } = \dfrac{ 6b - 7d }{ -6 }$ Solve for $b$.
Multiply both sides by the left denominator. $\dfrac{ 7b + 6c }{ -{4} } = \dfrac{ 6b - 7d }{ -6 }$ $-{4} \cdot \dfrac{ 7b + 6c }{ -{4} } = -{4} \cdot \dfrac{ 6b - 7d }{ -6 }$ $7b + 6c = -{4} \cdot \dfrac { 6b - 7d }{ -6 }$ Multiply both sides by the right denominator. $7b + 6c = -4 \cdot \dfrac{ 6b - 7d }{ -{6} }$ $-{6} \cdot \left( 7b + 6c \right) = -{6} \cdot -4 \cdot \dfrac{ 6b - 7d }{ -{6} }$ $-{6} \cdot \left( 7b + 6c \right) = -4 \cdot \left( 6b - 7d \right)$ Distribute both sides $-{6} \cdot \left( 7b + 6c \right) = -{4} \cdot \left( 6b - 7d \right)$ $-{42}b - {36}c = -{24}b + {28}d$ Combine $b$ terms on the left. $-{42b} - 36c = -{24b} + 28d$ $-{18b} - 36c = 28d$ Move the $c$ term to the right. $-18b - {36c} = 28d$ $-18b = 28d + {36c}$ Isolate $b$ by dividing both sides by its coefficient. $-{18}b = 28d + 36c$ $b = \dfrac{ 28d + 36c }{ -{18} }$ All of these terms are divisible by $2$ Divide by the common factor and swap signs so the denominator isn't negative. $b = \dfrac{ -{14}d - {18}c }{ {9} }$